Section
|
Mathematics
|
Title
|
Certain class of harmonic multivalent functions
|
Author(-s)
|
Eljamal E.A.a,
Darus M.b
|
Affiliations
|
Al Mergeb Universitya,
Universiti Kebangsaan Malaysiab
|
Abstract
|
Making use of the generalized derivative operator, we introduce a new subclass of harmonic multivalent functions. We obtain the coefficient bounds, distortion inequalities and inclusion relationships involving the neighborhoods of subclasses of harmonic multivalent functions.
|
Keywords
|
harmonic multivalent functions, derivative operator, neighborhood
|
UDC
|
517.53
|
MSC
|
30C45
|
DOI
|
10.20537/vm150309
|
Received
|
29 April 2015
|
Language
|
English
|
Citation
|
Eljamal E.A., Darus M. Certain class of harmonic multivalent functions, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 3, pp. 388-396.
|
References
|
- Clunie J., Sheil-Small T. Harmonic univalent functions, Ann. Acad. Sci. Fenn., Ser. A I, Math., 1984, vol. 9, pp. 3-25.
- Eljamal E.A., Darus M. A subclass of harmonic univalent functions with varying arguments defined by generalized derivative operator, Advance in Decision Sciences, 2012, vol. 2012, Article ID 610406, 8 p. http://dx.doi.org/10.1155/2012/610406
- Eljamal E.A., Darus M. Some properties of complex harmonic mapping, ISRN Applied Mathematics, 2012, vol. 2012, Article ID 587689, 6 p. http://dx.doi.org/10.5402/2012/587689
- Al-Shaqsi K., Darus M. On certain class of harmonic univalent functions, Int. J. Contemp. Math. Sci., 2009, vol. 4, no. 24, pp. 1193-1207.
- Al-Shaqsi K., Darus M. On harmonic univalent functions with respect to $k$-symmetric points, Int. J. Contemp. Math. Sci., 2008, vol. 3, no. 3, pp. 111-118.
- Al-Shaqsi K., Darus M. On harmonic functions defined by derivative operator, Journal of Inequalities and Applications, 2008, vol. 2008, Article ID 263413, 10 p. http://www.journalofinequalitiesandapplications.com/content/2008/1/263413
- Darus M., Al-Shaqsi K. On harmonic univalent functions defined by a generalised Ruscheweyh derivatives operator, Lobachevskii Journal of Mathematics, 2006, vol. 22, pp. 19-26.
- Al-Shaqsi K., Darus M. On a subclass of certain harmonic meromorphic functions, Far East Journal of Mathematical Sciences, 2006, vol. 20, issue 2, pp. 207-218.
- Eljamal E.A., Darus M. Inclusion properties for certain subclasses of $p$-valent functions associated with new generalized derivative operator, Vladikavkaz. Mat. Zh., 2013, vol. 15, no. 2, pp. 27-34.
- Salagean G.S. Subclass of univalent functions, Lecture Notes in Math., Berlin-Heidelberg-New York: Springer-Verlag, 1983, vol. 1013, pp. 362-372.
- Jahangiri J.M., Murugusundaramoorthy G., Vijaya K. Salagean-type harmonic univalent functions, Southwest J. Pure Appl. Math., 2002, issue 2, pp. 77-82.
- Silverman H. Harmonic univalent functions with negative coefficients, J. Math. Anal. Appl., 1998, vol. 220, issue 1, pp. 283-289.
- Silverman H., Silvia E.M. Subclasses of harmonic univalent functions, New Zealand J. Math., 1999, vol. 28, no. 2, pp. 275-284.
- Jahangiri J.M. Harmonic functions starlike in the unit disk, J. Math. Anal. Appl., 1999, vol. 235, no. 2, pp. 470-477.
- Ahuja O.P., Jahangiri J.M. Multivalent harmonic starlike functions, Ann. Univ. Mariae Curie-Sklodowska, Sect. A, 2001, vol. 55, pp. 1-13.
- Yasar E., Yalcin S. Neighborhood of a new class of harmonic multivalent functions, Computers and Mathematics with Applications, 2011, vol. 62, no. 1, pp. 462-473.
- Goodman A.W. Univalent functions and non-analytic curves, Proc. Amer. Math. Soc., 1957, vol. 8, no. 3, pp. 598-601.
- Ruscheweyh S. Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 1981, vol. 81, no. 4, pp. 521-527.
|
Full text
|
|